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A holographic data storage system using digital holography is proposed to record and retrieve multilevel complex amplitude data pages. Digital holographic techniques are capable of modulating and detecting complex amplitude distribution using current electronic devices. These techniques allow the development of a simple, compact, and stable holographic storage system that mainly consists of a single phase-only spatial light modulator and an image sensor. As a proof-of-principle experiment, complex amplitude data pages with binary amplitude and four-level phase are recorded and retrieved. Experimental results show the feasibility of the proposed holographic data storage system.
© 2016 Optical Society of America
1. Introduction
Optical data storage has a long lifetime for storing digital data and is economical with energy usage. Owing to the advantages, optical data storage is suitable for a data center and an archive storage system [1]. To further promote the use of optical data storage, it is necessary to make progress in expanding data capacity. In commercialized optical data storage, including CDs, DVDs, and Blu-ray Discs, data capacity has been improved by reducing a diffraction spot size. There are two ways to obtain a small diffraction spot: either by decreasing a wavelength, or by increasing a numerical aperture (NA) of a lens. These approaches, however, present technical obstacles in obtaining a smaller spot than that of Blu-ray Discs. Therefore it is required to develop a different optical data storage system for realizing large-capacity optical data storage.
Holographic data storage is one of the approaches for storing huge digital data, as compared with current optical data storage [2]. Digital data to be stored is encoded onto amplitude distribution of a beam using a spatial light modulator (SLM). The modulated beam interferes with a reference beam within a recording medium, which results in a volume hologram. In most of the conventional holographic storage systems, digital data are encoded onto the amplitude distribution alone. To increase the data capacity of holographic data storage, using amplitude and phase, complex amplitude distribution, as digital data is a promising approach [3, 4]. Holography is inherently capable of recording and retrieving complex amplitude distribution of a beam in a material. It is therefore possible to encode digital data onto not only amplitude distribution but also phase distribution in theory. However, to use complex amplitude distribution as digital data, a holographic data storage system requires to modulate and detect complex amplitude distribution.
Several researchers have developed modulation and detection techniques for complex amplitude distribution in a holographic data storage system. In general, to modulate complex amplitude distribution using current programmable devices, two SLMs are required [5]. Alternatively, the use of a single SLM and additional optical elements enables modulating complex amplitude distribution [6–8]. These techniques, however, make a holographic storage system large and complicated. Moreover, highly precise alignment technique is necessary to align optical components. In contrast, a recording system using a double phase hologram eliminates the need for the precise alignment technique [9, 10]. Although the double phase hologram can modulate complex amplitude distribution with a single phase-only SLM [11], the quality of a generated beam is degraded by an undesired zero order beam due to the imperfection of a current SLM [12].
For the detection of complex amplitude distribution, coherent addition [13] and the use of an additional optical component such as a birefringence plate [14], a lens array [15], or a grating [16] were proposed and demonstrated. Although these approaches reveals the phase information using an image sensor, the measurable complex amplitude values are restricted. Unlike these methods, using an interferometer allows the detection full complex amplitude values [4,17,18]. However, additional reference arm for phase-shifting interferometer increases the complexity of a holographic storage system.
In this paper, we propose a holographic data storage system using digital holography to record and retrieve multilevel complex amplitude data in a simple and compact optical system. Our proposed system mainly consists of a phase-only SLM and an image sensor. Unlike the above mentioned techniques, arbitrary complex amplitude distribution can be modulated and detected in the proposed system without additional components and reference arms because digital holography is capable of modulating and detecting complex amplitude distribution using current electronic devices.
This paper is organized as follows. In Section 2, a holographic data storage system using digital holography is described. In Section 3, we experimentally demonstrate a proposed system. Complex amplitude data pages are recorded and retrieved in a simple and compact optical setup. Finally, we provide our conclusion in Section 4.
2. Holographic data storage system using digital holography
In this Section, we describe a proposed holographic data storage system using digital holography. In the proposed system, digital data are encoded onto complex amplitude distribution. We refer to such data as a complex amplitude data page. Moreover, this amplitude and phase distributions are termed an amplitude data page and a phase data page, respectively. In the following subsections the processes of recording and retrieving complex amplitude data page are described in detail.
2.1. Recording process
Figure 1 shows a schematic of recording process in the proposed system. During recording process, a plane wave is modulated using a phase-only SLM. The phase-only SLM displays a computer-generated reference pattern (CGRP) [19] and an encoded phase pattern [20] for generating reference and signal beams, respectively. The CGRP is designed by an optimized calculation using a simulated annealing method which is well known for a design method of a computer-generated hologram (CGH) [21]. The use of a CGRP makes it possible to control a Fourier power spectrum, improving light efficiency and the quality of a reconstructed data page. More detailed descriptions of the CGRP can be found in [19] and [22]. In contrast, the encoded phase pattern is obtained using a linear phase encoding method [20] based on a phase CGH [23,24]. The encoding method allows us to generate a signal beam that contains arbitrary complex amplitude distribution using a single phase-only SLM. Let ad(x, y) and ϕd(x, y) denote amplitude and phase data pages, respectively. Figure 2 shows an encoded phase pattern for generating the complex amplitude data page ad(x, y) exp{ϕd(x, y)} shown in Fig. 1. This encoded phase pattern ψ is obtained on the basis of the following equations [23,24]:
where ϕlinear1 and ϕrand denote a linear phase pattern and a digital random phase mask, respectively. θ(ad) is a function to generate an arbitrary amplitude value ad on the basis of phase modulation, which satisfies [23,24] Since the phase shift π{1 − θ(ad)} in Eq. (1) is not significant in the case of that ad is binary, we ignore this term in the following. The linear phase pattern ϕlinear1 is used for separating a desired Fourier spectrum from unnecessary orders of a phase CGH [20,24] and an undesired zero order beam of an SLM [12]. In contrast, the digital random phase mask ϕrand is used for keeping the Fourier spectrum of a signal beam uniform regardless of the phase data page. For example, if a phase data page contains a constant single phase value without the digital random phase mask, there is a strong peak intensity on a recording medium. This leads to the degradation in a reconstructed data page and wastes the dynamic range of a recording medium [25]. The problem can be solved by introducing the digital random phase mask that has higher multilevel phase values than that of a phase data page.The phase-modulated beams from the CGRP and the encoded phase pattern are Fourier transformed by a lens. There are Fourier spectra of the CGRP and the encoded phase pattern in the Fourier plane, as shown in Fig. 3. The aperture removes undesired components of each Fourier spectrum. Note that the filtered spectrum in Fig. 3(d) corresponds to the Fourier spectrum of a desired complex amplitude distribution ad exp{i(ϕd + ϕlinear1 + ϕrand)}. The filtered Fourier spectra are imaged on a recording medium, and thus a volume hologram between signal and reference beams is recorded.
Fig. 3 Phase distribution on a phase-only SLM: (a) computer-generated reference pattern and (b) encoded phase pattern. (c) Fourier power spectrum of (a). (d) Fourier power spectrum of (b).
2.2. Retrieving process
Figure 4 shows a schematic of retrieving process in the proposed system. During retrieving process, a phase-only SLM displays the CGRP and a linear phase pattern ϕlinear2 for generating a phase-shifted beam shown in Fig. 5. The volume hologram in a recording medium is illuminated by the reference beam, and thereby the signal beam is reconstructed. At the same time, a phase-shifted beam propagates through a pinhole on an aperture and a recording medium. The reconstructed signal and the phase-shifted beams are incident on an image sensor, which results in a interference pattern, or a digital hologram. In this digital hologram, the summation of linear phase distribution ϕlinear1 and ϕlinear2 can be regarded as a single spatial frequency carrier. By using Fourier fringe analysis [26], it is possible to detect the complex amplitude distribution of a signal beam, or ad exp{i(ϕd + ϕrand)}. Note that spatial phase-shifting methods are also applicable to detect the complex amplitude distribution [27, 28]. Because the digital random phase mask ϕrand is a known parameter, it can be subtracted from the detected signal beam by signal processing. After the processing, the complex amplitude data page ad(x, y) exp{iϕd(x, y)} is retrieved, and hence the original digital data can be obtained.
Fig. 5 Phase-shifted beam. (a) Linear phase pattern for generating a phase shifted beam. (b) Fourier power spectrum of (a).
3. Experimental demonstration
In this Section, we experimentally demonstrate a holographic data storage system using digital holography to show that the proposed system enables us to record and retrieve complex amplitude data pages using a simple, compact, and stable optical setup. First, we show an experimental result of recording a single complex amplitude data page using the proposed system. Subsequently, we perform shift multiplexing of two complex amplitude data pages.
3.1. Single recording
Figure 6 shows an experimental setup for a holographic data storage system using digital holography. As a proof-of-principle demonstration, we recorded a single complex amplitude data page which consists of the amplitude and phase data pages shown in Figs. 7(a) and 7(b), respectively. The amplitude data page has binary amplitude values, 0 and 1, and is coded using a 3:16 coding for reducing interpixel crosstalk. In the 3:16 coding, a single symbol consists of three ON and thirteen OFF cells. The amplitude data page shown in Fig. 8(a) has 4×4 symbols. The phase data page has four-level phase values, 0, π/2, π, and 3π/2. Figure 7(c) shows a digital random phase mask having eight-level phase values. Because the phase level of the digital random phase mask is higher than that of the phase data page, the Fourier spectrum of a signal beam is uniformly spread and there are no high intensity peak values on a recording medium regardless of the phase data page.
Fig. 6 Experimental setup for demonstrating a holographic data storage system using digital holography.
Fig. 7 Complex amplitude data page: (a) amplitude data page and (b) phase data page. (c) Digital random phase mask.
Fig. 8 Experimental result and retrieving process of a complex amplitude data page. (a) Digital hologram. (b) Detected complex amplitude distribution of a signal beam from (a). (c) Complex amplitude values of the signal beam of (b) on a complex plane. (d) Complex amplitude values of the retrieved complex amplitude data page without a digital random phase mask.
Using Eq. (1), an encoded phase pattern was obtained from the complex amplitude data page and the digital random phase mask. The encoded phase pattern was subsequently placed on the center of the CGRP shown in Fig. 3(a). The resulting phase distribution was displayed on a phase-only SLM (X10468-01, Hamamatsu Photonics K. K.) with 800×600 pixels and a pixel pitch of 20 μm. A plane wave with a wavelength of 532 nm was incident on the SLM, and its phase distribution was modulated. The modulated beam was Fourier transformed by a lens. In the Fourier plane, an aperture removed undesired beams for generating signal and reference beams. The filtered beams i.e., signal and reference beams, were imaged on a photopolymer material (Kyoeisha Chemical Co.) with a thickness of 400 μm. As a result, a volume hologram between signal and reference beams was recorded within the material. During retrieving process, the volume hologram was illuminated by a reference beam, and thereby a signal beam was reconstructed. The signal beam interfered with a phase-shifted beam on a CCD camera with 1280×960 pixels and a pixel pitch of 4.65 μm.
Figure 8(a) shows a captured digital hologram. By using Fourier fringe analysis, the complex amplitude distribution of the signal beam was extracted. Figure 8(b) shows the complex amplitude distribution of a signal beam after the Fourier fringe analysis. For decoding the retrieved data, the complex amplitude distribution was divided into 16×16 areas which correspond to the number of cells in the complex amplitude data page shown in Figs. 7(a) and 7(b). The complex amplitude values in each area were averaged and plotted on a complex plane, as shown in Fig. 8(c). The averaged complex values contains the phase values of the digital random phase mask.
By subtracting the phase values of the digital random phase mask from the averaged complex amplitude values, it is possible to purely obtain the information of the complex amplitude data page. Figure 8(d) shows the averaged complex amplitude values without the digital random phase mask on a complex plane. The amplitude values are normalized by the maximum amplitude value of the retrieved amplitude data page. The squares and circles denote recorded and retrieved data, respectively. By decoding each retrieved data as the nearest neighbor recorded data on a complex plane, we were able to readout the original complex amplitude data page without error.
Note that there is phase distortion on a reconstructed signal beam due to the imperfection and misalignment of optical components. In addition, the refractive index mismatch between a medium and an air leads to the spherical aberration [29]. These phase distortion can be compensated by detecting the phase distribution of a known complex amplitude data page or a blank data page on an image sensor plane before recording and retrieving processes. Although we do not describe a detailed compensation procedure, a lot of compensation techniques can be found in the field of phase imaging, in particular digital holographic microscopy [30,31].
3.2. Shift multiplexing
To show the capability of multiplexed recording in the proposed system, we recorded two complex amplitude data pages shown in Fig. 9 using a shift multiplexing method. Shift multiplexing, one of the multiplexed recording methods, enables multiple volume hologram to be partially overlapped and stored in a recording medium by slightly displacing a recording medium. Before implementing the shift multiplexing, we evaluated shift selectivity to determine a recording pitch of volume holograms. The shift selectivity is the relationship between the intensity of the reconstructed data and the shift pitch of a recording medium, which provides us with the guideline and insights for shift multiplexing.
Shift selectivity was experimentally obtained as follows. Using the experimental setup shown in Fig. 6, the volume hologram of a single complex amplitude data page shown in Fig. 9(a) was recorded in the material. After that, the hologram was illuminated by the reference beam. In this experiment, the linear phase pattern for generating a phase-shifted beam was not used because the phase information of a signal beam is not significant and only the intensity of a reconstructed signal beam is of interest. The intensity of the retrieved signal beam was detected using a CCD camera. Subsequently, a recording medium, which was set on a stage, was displaced in the direction perpendicular to the optical axis. Figure 10 shows the obtained shift selectivity of the complex amplitude data page 1 and typical reconstructed images. Minimum intensity values are obtained at 4, 8, and 12 μm. In these positions the effect of interpage crosstalk is small. Note that the shift selectivity of the complex amplitude data page 2 is similar to that of the complex amplitude data page 1 because shift selectivity is manly determined by a reference beam [32,33].
We recorded two complex amplitude data pages shown in Fig. 9 using a shift multiplexing method. Each data page was superimposed on the digital random phase mask and was encoded using the linear phase encoding method. Using each of encoded phase patterns, volume holograms were recorded in the material at intervals of 12 μm at which the effect of crosstalk is small as shown in Fig. 10. During retrieving process, each volume hologram was illuminated by the reference beam. The CCD camera captured each digital hologram. Figures 11(a) and 11(b) show extracted complex amplitude distribution of reconstructed signal beams from digital holograms after the Fourier fringe analysis. By averaging the complex amplitude values and subtracting the digital random phase mask, the complex amplitude values are obtained, as shown in Figs. 11(c) and 11(d). In each complex plane, the amplitude values are normalized by the maximum amplitude value of each retrieved amplitude data page. In comparison with the experimental result of single recording shown in Fig. 8(d), the complex amplitude values tends to be widely spread from the recorded data on a complex plane. This is caused by the interpage crosstalk and distortion of volume holograms due to overlapping. Although there is distortion in retrieved data, the original data pages can be retrieved without data error by decoding each complex amplitude value. The experimental results show that the proposed system allows us to record and retrieve complex amplitude data pages in a simple and compact optical setup.
Fig. 11 Experimental results of shift multiplexing. The complex amplitude distribution of detected signal beams of (a) data page 1 and (b) data page 2. Retrieved complex amplitude values without a digital random phase mask of (c) data page 1 and (b) data page 2.
4. Conclusion
We have proposed and demonstrated a holographic storage system using digital holography. The research presented here is the extension of our preliminary studies in [34] and [35]. These numerical and experimental studies have shown that a single binary phase data page can be recorded by using digital holographic techniques. In contrast to these preliminary studies, we successfully recorded and retrieved multilevel complex amplitude data pages using a shift multiplexing method in this paper. In addition, we introduced a digital random phase mask to a holographic data storage system for keeping the Fourier power spectrum of a signal beam uniform regardless of a phase data page.
Our proposed system is similar to a collinear setup [36] which is well known for a simple and compact holographic storage system. The collinear setup has designed for recording just amplitude data pages with a single SLM. In contrast to the collinear system, it is possible to modulate complex amplitude distribution in the proposed system by using a single phase-only SLM and a CGH technique. In addition, complex amplitude distribution can be detected using a common-path interferometer and digital holography. The use of such digital holographic techniques allows us to develop a simple, compact, and stable optical setup.
In comparison with conventional holographic data storage systems which records only amplitude data pages, the proposed system increases the dimension for data coding by introducing phase data pages. Therefore there is a possibility of expanding the data capacity of holographic data storage. For achieving large capacity in the proposed system, it is required to choose and optimize data coding methods taking into account the noise such as interpage and interpixel crosstalk.
Funding
Japan Society for the Promotion of Science (JSPS) (15J11996).
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